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TRS Innermost pair #487092964
details
property
value
status
complete
benchmark
#4.32.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0169099 seconds
cpu usage
0.017551
user time
0.004826
system time
0.012725
max virtual memory
113188.0
max residence set size
4264.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) F(x:S,c(y:S)) -> F(x:S,s(f(y:S,y:S))) F(x:S,c(y:S)) -> F(y:S,y:S) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) Problem 1: SCC Processor: -> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) F(x:S,c(y:S)) -> F(x:S,s(f(y:S,y:S))) F(x:S,c(y:S)) -> F(y:S,y:S) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) ->->-> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->->Cycle: ->->-> Pairs: F(x:S,c(y:S)) -> F(y:S,y:S) ->->-> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: F(s(x:S),s(y:S)) -> F(x:S,s(c(s(y:S)))) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Projection: pi(F) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: F(x:S,c(y:S)) -> F(y:S,y:S) -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Projection: pi(F) = 2 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: f(s(x:S),s(y:S)) -> f(x:S,s(c(s(y:S)))) f(x:S,c(y:S)) -> f(x:S,s(f(y:S,y:S))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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